Question: Simplify the following expression: $ x = \dfrac{k - 4}{7k} - \dfrac{1}{2} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{k - 4}{7k} \times \dfrac{2}{2} = \dfrac{2k - 8}{14k} $ Multiply the second expression by $\dfrac{7k}{7k}$ $ \dfrac{1}{2} \times \dfrac{7k}{7k} = \dfrac{7k}{14k} $ Therefore $ x = \dfrac{2k - 8}{14k} - \dfrac{7k}{14k} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{2k - 8 - 7k }{14k} $ Distribute the negative sign: $x = \dfrac{2k - 8 - 7k}{14k}$ $x = \dfrac{-5k - 8}{14k}$